In reply to Coel Hellier:
In the teaching statement that I had to write for professorial job applications I stressed the importance of teaching a largeish syllabus of facts first, even if this may look decidedly old fashioned.
All this modern emphasis on "problem oriented learning" or "skills" can come later. IMO, for this to be productive the students must have first acquired a body of knowledge that they can then use to quickly check any claims arising from the explanations they develop for the question/problem they are given.
In my field of research, the immediate focus on molecular biology - at the cost of other disciplines even including genetics, never mind old fashioned zoology - in the background training of our grad students is becoming a huge problem.
However, before you can even start doing proper biology you will need solid maths skills, and the foundations for this must be laid in school, ideally starting in primary school. However, school maths is largely being reduced to arithmetics, i.e. using a pocket calculator.
I guess the reason for this is that we are much too lenient with celebrities bragging on TV about how they were always bad at maths. In a way they are messing with our kids´ brains. Instead we should be demonstrating that maths may be hard but getting to the core of problems can be fun, and is in any case useful whatever you will do later.
This whole "bad at maths" culture should be treated the same way as if someone claimed they couldn´t read: Yes, maths may not be your strength, but better do something about it rather than celebrate your deficit, it is nothing to be proud of, here is help...
CB